[andredieb]

This is great to hear! I used a similar construction on my final project (electrical engineering) but left the appropriate mathematical proof (if any) into the Future Works section. The classification rule I found to be better was:

  c = argmax_{c \in C} (log(P(c)) + Sum_i (N_{d,d_i} \times log(P(d_i|c)))

where

  c - best class
  C - set of classes
  P(c) - prior prob. of class c
  P(d_i|c) - conditional of the word d_i on the class c and
  N_{d,d_i} - frequency of word d_i in document d

Excuse me for the possibly weird notation.

Virtually this expression means it places a frequency power upon the word probability, which is basically assuming (naively, I think) "words that are more likely to occur should be empowered".